Chapter 6.2, Problem 8E

To determine

To evaluate: The given integral

Answer to Problem 8E

The value of the given integral is $-80$

Explanation of Solution

Given Information:

The integral ${\displaystyle \underset{3}{\overset{7}{\int }}(-20)dx}$

Formula Used:

The integration of dx is given by,

  ${{\displaystyle {\int }_a^{b}dx=\left[x\right]}}_a^b$

Calculation The given expression represents a definite integral where the differential variable dx is to be integrated with the limits of integration being [3, 7].

Considering the given integral,

  $\begin{array}{c}{\displaystyle \underset{3}{\overset{7}{\int }}(-20)dx}=-20{\displaystyle \underset{3}{\overset{7}{\int }}dx}\\ =-20{\left[x\right]}_3^7\\ =-20\times \left(7-3\right)\\ =-80\end{array}$

Thus, ${\displaystyle \underset{3}{\overset{7}{\int }}(-20)dx}=-80$